论文标题
凸量化保留logconcavity
Convex Quantization Preserves Logconcavity
论文作者
论文摘要
logconcave的可能性对于适当的统计推断与凸成本函数一样重要，对于变分优化很重要。编写似然模型时，通常会忽略量化，而忽略用于收集数据的物理探测器的局限性。这两个事实提出了一个问题：可能在可能性模型中包括量化吗？真实数据的可能性是logconcave吗？我们提供了一个普遍的证据，即导致LogConcave连续数据可能性的同样简单假设也导致LogConcave量化量化数据，但前提是使用凸量化区域。
A logconcave likelihood is as important to proper statistical inference as a convex cost function is important to variational optimization. Quantization is often disregarded when writing likelihood models, ignoring the limitations of the physical detectors used to collect the data. These two facts call for the question: would including quantization in likelihood models preclude logconcavity? are the true data likelihoods logconcave? We provide a general proof that the same simple assumption that leads to logconcave continuous-data likelihoods also leads to logconcave quantized-data likelihoods, provided that convex quantization regions are used.
